Optical vortices constitute a great family of light fields, which is actively studied over 30 years (Shen et al. in Light Sci Appl 8:90, 2019). The studies include various aspects, including direct generation in lasers (Lin et al. in Opto-Electron Adv 4:210006, 2021), interaction with matter (Zhang et al. in Opto-Electron Adv 5:210066, 2022), propagation and focusing (Zhang et al. in Opto-Electr Adv 5:210066, 2022). Light fields with optical vortices are usually characterized by the orbital angular momentum (OAM) (Allen et al. in Phys Rev A 45:8185–8189, 1992) and the topological charge (TC) (Berry in J Opt A Pure Appl Opt. 6:259–268, 2004). In a number of studies, the topological charge (TC) of a superposition of parallel optical vortices (OVs), and in particular, parallel Laguerre-Gaussian (LG) beams, was studied. This problem has been of interest since 2000, when the number and location of OVs in a superposition of two parallel Gaussian beams with embedded OVs were studied in Molina-Terriza et al. (Opt Lett 25:1135–1137, 2000). In Molina-Terriza et al. (Opt Lett 25:1135–1137, 2000), a transcendental equation was obtained analytically for determining the position of OVs. However, it is applicable only for the case when the vortices in both beams are of the first order. It is also shown that when two beams are separated by a certain critical distance, negative-order vortices appear along with positive-order vortices. Later, in Pyragaite et al. (Lithuan J Phys 47:21–26, 2007), using the analysis of forks in the interference pattern of two parallel LG beams, it was shown that when varying of the distance between the beams changes the arrangement of screw dislocations in the superposition. In addition, the same authors (Pyragaite and Stabinis in Opt Commun 213:187–191, 2002) showed that the number of vortices in the superposition of two parallel LG beams can change during propagation in space, although the total TC remains unchanged. In Lopez-Mago et al. (J Opt 15:044028, 2013), the superposition of two off-axis optical vortices, but with orthogonal polarization, is studied. Instead of the dynamics of phase singularities, this paper studied the dynamics of polarization singularities and the position of C-points as a function of the distance between vortices, their TC, and the phase delay between them. In Naik and Viswanathan (J Opt 18:095601, 2016), the interference of two off-axis Gaussian beams with different curvature of the wave front is also considered. The conditions for vortex dipoles (two OVs of opposite orders) formation are obtained. In Cheng and Lü (J Mod Opt 55:2751–2764, 2008), the coherent and the incoherent superposition of two parallel partially coherent OVs is studied. It is shown that the type of superposition, the distance between the beams, the propagation distance, and the coherence parameter affect the number and location of coherence vortices. The number of vortices, however, is determined only numerically. Study Sukhorukov et al. (Phys Rev E 66:036608, 2002) considered OVs which are formed in a superposition of off-axis vortices while a nonlinear process of three-wave mixing. The number of vortices and their TCs have been established in some particular cases. In a recent article (Zhang et al. in Phys Scr 96:125105, 2021), the interaction of parallel Bessel-Gaussian beams is considered. The dependence of formation, annihilation and splitting of OVs on the displacement of the beams from the optical axis, on their TC, and on the phase difference between them is studied. It is shown that the total TC of such a composite field is not necessarily equal to the sum of the TCs of the composite beams. In Kotlyar et al. (Opt Express 29:42962–42977, 2021), it was shown how to calculate the TC of a superposition of only two parallel LG beams. In particular, in Kotlyar et al. (Opt Express 29:42962–42977, 2021) it was analytically shown that if two beams have the same TC, for example, m, then the superposition of such beams with arbitrary distance between them will also have a TC equal to m.